Producing three-dimensional hardcopies using a computer is well known in the art. To do this, a three-dimensional image is printed on a planer sheet in two dimensions, but a viewer, under certain circumstances, perceives the image as three-dimensional. For example, an article by Daniel J. Sandin et al., "Computer Generated Barrier Strip Autostereography" presented at the Symposium on Electronic Imaging (SEI) in 1989 discusses the computer graphics transformations necessary to produce three-dimensional images for lenticular systems and computational processes to combine different views onto a three-dimensional image. A lenticular system typically includes a sheet of cylindrical lenses, called lenticules (described below), positioned on a flat picture at the focal plane of the lenses. The Sandin reference teaches that by connecting a computer to a high-resolution output scanner, computer-based images, i.e. images designed using a computer, and digitized camera images, i.e. images created with the use of a camera and digitized by a computer, can be automatically combined and printed on transparency film.
In addition to generating images for three-dimensional transformation by the computer, such images can be input into the computer using video cameras or image scanners. In either method, a spatial sequence of frames is automatically digitized and stored by the computer as seen in step 100 of FIG. 10. A particular point common to all the frames, for example point 108 in step 101, the center of depth, is determined. The distance between the origin of a coordinate system and the same image point on two simultaneous frames determines the degree of motion. Referring to step 101, point 108 on ball 109 appears on the left of frame 106 and on the right in frame 107. Hence, ball 109 is interpreted by the computer as "moving" from the left to the right.
Subsequent off-axis perspective projections of the image are done to the right and left from this center of depth as indicated in step 102. The degree of off-axis projection determines the depth an observer sees when viewing the hardcopy. The computer requires at least two images from different perspectives to provide a hardcopy which creates the illusion of three-dimensional vision. The more image data provided to the computer, the better the resulting "three-dimensional" hardcopy.
Once a graphical model is developed, the computer's software allows the viewer to determine the desired viewing angle by rotating the image on a CRT monitor until an angle is found that is aesthetically pleasing. Depth information is also determined by the viewer at this time. To give the illusion of depth, an off-axis perspective projection of the image is created both to the left and to the right about its center of depth. The degree of off-axis projection determines the depth an observer sees when viewing the resulting hardcopy. The resulting images are then stored for subsequent processing as indicated in step 103. The computer converts these images into alternating, thin vertical strips in a process called "interleaving". A composite is formed of these thin interleaved strips. For example, as shown in step 104, if three images from different perspectives were provided, a composite of these images would begin with a strip from the first image A, then the second image B, and finally the third image C. This sequence would be repeated until all three images were totally interleaved. A typical composite may have ten images interleaved.
The composite information is fed to a hardcopy output device, such as a laser printer, which is indicated in step 105. The composite information is printed as an interleaved image on standard paper and then laminated with a lenticular screen. A typical lenticular surface, shown in FIG. 8, consists of narrow (generally less than 0.3 mm), cylindrical plastic lenses 80, called lenticules, which run parallel to the vertical sides 81 of the interleaved image surface 82.
Lenticule 80 ensures that light from source 83 scattered from any point, for example point 85, on the interleaved image surface 82 is parallel. The direction that light emerges, see light rays 84, from the lenticule 80 depends on the location of the point of reflection, i.e. point 85, on the interleaved image plane 82. In this manner, multiple images may be seen depending on the viewing angle. The number of images seen in the hardcopy corresponds to the number of images interleaved to form the composite.
However, because of inherent distortions or inaccuracies in lenticular lenses, images previously produced using stereoscopic methods have yielded blurred images.